Function lupnt::RatioOfSectorToTriangleArea

Function Documentation

Real lupnt::RatioOfSectorToTriangleArea(const Vec3 &r1, const Vec3 &r2, Real tau)

Ratio eta of the area of the orbital sector swept between two position vectors to the area of the triangle they form with the focus, for a given time-of-flight tau (Gauss’s sector-triangle ratio, solved via Hansen’s method).

Used by conversions/state_conversions.cc (Gauss/Lambert-style position-velocity conversion, e.g. converting two position vectors plus a transfer time into a state vector) as part of the Herrick-Gibbs/Gauss orbit-determination calculation.

Parameters:

  • r1 – First position vector [any consistent length unit]

  • r2 – Second position vector [same unit as r1]

  • tau – Time of flight between r1 and r2, scaled per Montenbruck & Eberhard’s convention [consistent time unit]

Returns:

Sector-to-triangle area ratio eta; throws if Hansen’s iteration does not converge O. Montenbruck and G. Eberhard, Satellite orbits: models, methods, and applications. Berlin : New York: Springer, 2000. doi: 10.1007/978-3-642-58351-3.